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URL: https://oeis.org/A303111

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A303111
Array read by antidiagonals: T(m,n) = number of total dominating sets in the grid graph P_m X P_n.
7
0, 1, 1, 3, 9, 3, 4, 25, 25, 4, 5, 81, 161, 81, 5, 9, 289, 961, 961, 289, 9, 16, 961, 6235, 11236, 6235, 961, 16, 25, 3249, 39601, 137641, 137641, 39601, 3249, 25, 39, 11025, 251433, 1677025, 3270375, 1677025, 251433, 11025, 39
OFFSET
1,4
COMMENTS
Equivalently, the number of n X m binary matrices with every element adjacent to some 0 horizontally or vertically.
LINKS
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
EXAMPLE
Table begins:
=======================================================================
m\n| 1 2 3 4 5 6 7
---|-------------------------------------------------------------------
1 | 0 1 3 4 5 9 16 ...
2 | 1 9 25 81 289 961 3249 ...
3 | 3 25 161 961 6235 39601 251433 ...
4 | 4 81 961 11236 137641 1677025 20430400 ...
5 | 5 289 6235 137641 3270375 76405081 1783064069 ...
6 | 9 961 39601 1677025 76405081 3416753209 152598828321 ...
7 | 16 3249 251433 20430400 1783064069 152598828321 13057656650476 ...
...
CROSSREFS
Rows 1..2 are A195971(n-1), A141583(n+1).
Main diagonal is A133793.
Cf. A218354 (dominating sets), A291872 (connected dominating sets).
Cf. A303114 (king graph), A303118 (minimal total dominating sets).
Sequence in context: A201416 A072560 A290506 * A299633 A393360 A074959
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 18 2018
STATUS
approved